Posted by Shinji Langley on Friday, July 16, 2010 at 11:35am.
A quick question to check my answer.
Trains A & B are travelling in the same direction on parallel tracks. Train A is travelling at 100 miles per hour and train B is travelling at 110 miles per hour. Train A passes a station at 2:10 A.M. If train B passes the same station at 2:40 A.M., at what time will train B catch up to train A?
My answer is 7:40 A.M.
Here is my reasoning:
Train A is ahead of Train B by 30 minutes.
This means that by the time train B gets to the station, train A would have travelled 50 miles.
So every hour that Train A travels, Train B closes the gap because it is 10 miles an hour faster.
If I start their time at 2:40 A.M., here is what I come up with:
Time/TrainA/TrainB
2:40/50/0
3:40/150/110
4:40/250/220
5:40/350/330
6:40/450/440
7:40/550/550 < Both trains would have travelled the same distance by 7:40.
Can someone double check. Thanks.

Math Algebra  Reiny, Friday, July 16, 2010 at 11:53am
your answer is correct
an easier way is the following:
let the time past 2:10 be t hours
so when they pass each other , the slower train has gone for t hours and the faster train for 11/2 hrs.
so 110(t1/2) = 100t
10 t = 55
t = 5.5 hrs or 5 hours and 30 min
add that to 2:10 to get 7:40